How to beat a presupp at their own game

[Angrboda]

To fellow atheists, somewhat different question - but a question I often see from theists. The question goes : where do atheists get their basis to justify any claim they make?

There is a whole field of philosophy devoted to this. It's called "epistemology." It is a matter of rigorous debate upon what basis we have knowledge.

A pretty solid theory is correspondence theory. It says that knowledge is a "justified true belief." 

Just to be precise, the correspondence theory is a theory of truth, not knowledge. According to correspondence theory, what makes something true is that it corresponds to a state of affairs in reality. There are other theories of truth. The justified true belief bit I believe started with Plato, and it's long been known to be inadequate, but it get's the lion's share of what needs to be in a definition of knowledge right. For a bit about the inadequacy, look into the Gettier problem.